1. Set Theory Using Mathematics to Classify Objects 2 © 2010 Pearson Education, Inc. All rights reserved.

2. Survey Problems © 2010 Pearson Education, Inc. All rights reserved.Section 2.4, Slide 2 2.4 Label sets in Venn diagrams with various names Use Venn diagrams to solve survey problems Understand how to handle contradictory information in survey problems

3. © 2010 Pearson Education, Inc. All rights reserved.Section 2.4, Slide 3 Naming Venn Diagrams We use set notation to name regions of a Venn diagram.

4. © 2010 Pearson Education, Inc. All rights reserved.Section 2.4, Slide 4 Naming Venn Diagrams Example: Name r 2.

5. © 2010 Pearson Education, Inc. All rights reserved.Section 2.4, Slide 5 Survey Problems When we collect and organize data into sets, we usually want to analyze the information. These types of problems are called survey problems.

6. © 2010 Pearson Education, Inc. All rights reserved.Section 2.4, Slide 6 Survey Problems Example: A television network conducted a market survey. The following information on viewing habits was obtained. (continued on next slide) Determine how many people do not want to see reality shows and how many prefer to watch TV on the weekend?

7. © 2010 Pearson Education, Inc. All rights reserved.Section 2.4, Slide 7 Survey Problems Solution: The universal set contains three subsets. (continued on next slide)

8. © 2010 Pearson Education, Inc. All rights reserved.Section 2.4, Slide 8 Survey Problems Solution: Condition (a): there are 3 people in (continued on next slide)

9. © 2010 Pearson Education, Inc. All rights reserved.Section 2.4, Slide 9 Survey Problems Solution: Condition (b): there are 14 people in (continued on next slide)

10. © 2010 Pearson Education, Inc. All rights reserved.Section 2.4, Slide 10 Survey Problems Solution: Condition (d): 8 people want to see weekday reality shows, so 5 people have not been counted in Condition (c): 18 have not been counted in (continued on next slide)

11. © 2010 Pearson Education, Inc. All rights reserved.Section 2.4, Slide 11 Survey Problems Solution: Condition (e): there are 12 more members in W, 4 more in E, and 14 more in R. Condition (h): there are 13 people outside {W, R, E}. (continued on next slide)

12. © 2010 Pearson Education, Inc. All rights reserved.Section 2.4, Slide 12 Survey Problems Solution: Do not want to see reality shows = 12 + 11 + 4 + 13 = 40 Prefer to watch TV on weekend =14 + 18 + 4 + 13 = 49

13. © 2010 Pearson Education, Inc. All rights reserved.Section 2.4, Slide 13 Contradictions in Survey Problems A survey problem may contain contradictory information. Example: What web browsers are used by a sample of people? (continued on next slide)

14. © 2010 Pearson Education, Inc. All rights reserved.Section 2.4, Slide 14 Contradictions in Survey Problems Solution: 212 + 374 = 586 use only one of the two browsers. Contradicts (d).

15. © 2010 Pearson Education, Inc. All rights reserved.Section 2.4, Slide 15 Data in Tabular Form Example: A company sells Pilates videos. How do customers wish to purchase the videos? Via Access Code = web download of video (a) Find the number of elements in (b) Find the number of elements in (continued on next slide)

16. © 2010 Pearson Education, Inc. All rights reserved.Section 2.4, Slide 16 Data in Tabular Form Example: A company sells Pilates videos. How do customers wish to purchase the videos? Via Access Code = web download of video (a) (b)